How Is A Random Variable Is Related To Probability Distribution?

Random variable has been defined as a 'function' which assumes real value on the outcomes of a random experiment. In repeated performances of the random experiment, the random variable will in general assume different values with a definite probability associated with each value or interval of values.

Probability Distribution (or simply distribution) of a random variable is a statement specifying the set of its possible values together with their respective probabilities. When a random experiment is theoretically assumed to serve as a model, the probabilities can be given as a function of the random variable. The probability distribution concerned is then generally known as theoretical distribution including Binomial distribution, Poisson distribution, Hypergeometric distribution, and Normal distribution.